1. Field of Invention
This invention relates to signal processing and pattern recognition, specifically to a new way of characterization of data as being generated by dynamical systems evolving in time and space.
2. Discussion of Prior Art
Our invention is based on novel ideas in signal processing derived by us from the theory of dynamical systems. This field is relatively new, and we specifically have developed our own theoretical framework which makes our approach unique. While we do not include the full theory here, it gives our invention a solid analytical foundation.
The theory of dynamically-based detection and classification is still under active the oretical development. The main idea of our approach is to classify signals according to their dynamics of evolution instead of particular data realizations (signal measurements). Our method opens the possibility of a very compact and robust classification of signals of deterministic origin.
Modeling of dynamical systems by ordinary differential equations and discrete maps reconstructed from data has been proposed by several researchers, and their results have been published in open scientific journals (for example, J. P. Crutchfield and B. S. McNamara, Complex Systems 1(3), p.417 [8]). Modeling can generally be performed on low-noise data when very accurate dynamical models can be found to fit the data. This may be considered a prior art, though in the current invention we do not use parametric dynamical systems to model data, rather we use them for detection and classification-of signals. Correspondingly, in the high noise case, our model equations need not necessarily be exact, since we do not try to use the estimated equations to predict the data. This makes an important difference between modeling approaches proposed in the prior art and our detection/classification framework: while model selection is subject to numerous restrictions, our algorithmic chain can always be implemented, regardless of the source of the signal. Currently, no practical devices or patents exist using this technology.
Note: in all references throughout this document, we use the term xe2x80x9csignalsxe2x80x9d to mean the more general category of xe2x80x9ctime series, signals, or imagesxe2x80x9d.
Accordingly, several objects and advantages of our invention are:
1. to provide a theoretically well-founded method of signal processing and time series analysis which can be used in a variety of applications (such as Sonar, Radar, Lidar, seismic, acoustic, electromagnetic and optic data analysis) where deterministic signals are desired to be detected and classified;
2. to provide possibilities for both software-based and hardware-based implementations;
3. to provide compatibility of our device with conventional statistical and spectral processing means best-suited for a particular application;
4. to provide amplitude independent detection and classification for stationary, quasi-stationary and non-stationary (transient) signals;
5. to provide detection and classification of signals where conventional techniques based on amplitude, power-spectrum, covariance and linear regression analyses perform poorly;
6. to provide recognition of physical systems represented by scalar observables as well as multi-variate measurements, even if the signals were nonlinearly transformed and distorted during propagation from a generator to a detector;
7. to provide multi-dimensional feature distributions in a correspondingly multi-dimensional classification space, where each component (dimension) corresponds to certain linear or nonlinear signal characteristics, and all components together characterize the underlying state space topology for a dynamical representation of a signal class under consideration;
8. to provide robust decision criteria for a wide range of parameters and signals strongly corrupted by noise;
9. to provide real-time processing capabilities where our invention can be used as a part of field equipment, with on-board or remote detectors operating in evolving environments;
10. to provide operational user environments both under human control and as a part of semi-automated and fully-autonomous devices;
11. to provide methods for the design of dynamical filters and classifiers optimized to a particular category of signals of interest;
12. to provide a variety of different algorithmic implementations, which can be used separately or be combined depending on the type of application and expected signal characteristics;
13. to provide learning rules, whereby our device can be used to build and modify a database of features, which can be subsequently utilized to classify signals based on previously processed patterns;
14. to provide compression of original data to a set of model parameters (features), while retaining essential information on the topological structure of the signal of interest; in our typical parameter regimes this can provide enormous compression ratios on the order of 100:1 or better.
Further objects and advantages of our invention will become apparent from a consideration of the flowcharts and the ensuing description.